Simplical structures of knot complements

Aleksandar Mijatovic
2005 Mathematical Research Letters  
It was shown in [7] that there exists an explicit bound for the number of Pachner moves needed to connect any two triangulation of any Haken 3-manifold which contains no fibred sub-manifolds as strongly simple pieces of its JSJ-decomposition. In this paper we prove a generalisation of that result to all knot complements. The explicit formula for the bound is in terms of the numbers of tetrahedra in the two triangulations. This gives a conceptually trivial algorithm for recognising any knot
more » ... ising any knot complement among all 3-manifolds.
doi:10.4310/mrl.2005.v12.n6.a6 fatcat:5fhpqoklgzfk5coldk5b6havue